Mathematische Annalen

, Volume 302, Issue 1, pp 609–686 | Cite as

On thep-adic height of Heegner cycles

  • Jan Nekovář


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  1. [At-Le]
    Atkin, A.O.L., Lehner, J.: Hecke operators onΓ 0(m), Math. Ann.185, 134–160 (1970)Google Scholar
  2. [At-Li]
    Atkin, A.O.L., Li, W.: Twists of Newforms and Pseudo-Eigenvalues ofW-Operators, Invent. Math.48, 221–243 (1978)Google Scholar
  3. [Be]
    Beilinson, A.A.: Height pairing between algebraic cycles, in:K-theory, Arithmetic and Geometry; Seminar, Moscow 1984–86 (Manin, Yu.I., ed.), Lect. Notes in Math.1289, Springer, Berlin, Heidelberg, New York, 1987, pp. 1–26Google Scholar
  4. [Ber]
    Berthelot, P.: Remarks on Faltings' approach to theC cris conjecture, preprint Rennes, June 21, 1994Google Scholar
  5. [Bl-Ka]
    Bloch, S., Kato, K.:L-functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift I. Progress in Mathematics86, Birkhäuser, Boston, Basel, Berlin, 1990, pp. 333–400Google Scholar
  6. [Br]
    Brylinski, J.-L.: Heights for local systems on curves, Duke Math. J.59, 1–26 (1989)Google Scholar
  7. [B-F-H]
    Bump, D., Friedberg, S., Hoffstein, J.: Nonvanishing theorems forL-functions of modular forms and their derivatives, Invent. Math.102, 543–618 (1990)Google Scholar
  8. [Ca]
    Carayol, H.: Sur les représentationsl-adiques, attachées aux formes modulaires de Hilbert, Ann. Sci. Ec. Norm. Supér.19, 409–469 (1986)Google Scholar
  9. [De 1]
    Deligne, P.: Formes modulaires et représentations ℓ-adiques, in: Séminaire Bourbaki, No 355, Lect. Notes in Math,179, Springer, Berlin, Heidelberg, New York, 1971, pp. 139–172Google Scholar
  10. [De 2]
    Deligne, P.: La conjecture de Weil II, Publ. Math. de l'I.H.E.S.52, 137–252 (1980)Google Scholar
  11. [Fa]
    Faltings, G.: Crystalline cohomology andp-adic Galois representations, in: Algebraic Analysis, Geometry, and Number Theory (Igusa, J.-I., ed.), John Hopkins University Press, Baltimore, 1990, pp. 25–79Google Scholar
  12. [Fo-Me]
    Fontaine, J.-M., Messing, W.:p-adic periods andp-adic étale cohomology, in: Current Trends in Arithmetic Algebraic Geometry. Contemporary Mathematics67, American Mathematical Society, Providence, Rhode Island, 1987, pp. 179–207Google Scholar
  13. [Fo-PR]
    Fontaine, J.-M., Perrin-Riou, B.: Autour des conjectures de Bloch et Kato: cohomologie galoisienne et valeurs de fonctions L, in: Motives, Proceedings of AMS Summer Research Conference held in July 1991, Seattle, Proceedings of Symposia in Pure Mathematics55/I, American Mathematical Society, Providence, Rhode Island, 1994, pp. 599–706Google Scholar
  14. [Gre]
    Greenberg, R.: Iwasawa Theory forp-adic Representations, in: Algebraic Number Theory, in honor of K. Iwasawa, Advanced Studies in Pure Mathematics, Academic Press, Boston, 1989, pp. 97–137Google Scholar
  15. [Gro]
    Gros, M.: Régulateurs syntomiques et valeurs de fonctionsL p-adiques I, Invent. Math.99, 293–320 (1990)Google Scholar
  16. [Gr]
    Gross, B.H.: Heegner points onX 0(N), in: Modular Forms (Rankin, R.A., ed.), Ellis Horwood, Chichester, 1984, pp. 87–106Google Scholar
  17. [Gr-Za]
    Gross, B.H., Zagier, D.B.: Heegner points and derivatives ofL-series, Invent. Math.84, 225–320 (1986)Google Scholar
  18. [G-K-Z]
    Gross, B.H., Kohnen, W., Zagier, D.B.: Heegner points and derivatives ofL-series II, Math. Ann.278, 497–562 (1987)Google Scholar
  19. [Ha]
    Hatcher, R.L.: Heights andL-series, Canad. J. Math.XLII, 533–560 (1990)Google Scholar
  20. [Hi 1]
    Hida, H.: Ap-adic measure attached to the zeta functions associated with two elliptic modular forms. I, Invent. Math.79, 159–195 (1985)Google Scholar
  21. [Hi 2]
    Hida, H.: Ap-adic measure attached to the zeta functions associated with two elliptic modular forms. II, Ann. Inst. Fourier38, 1–83 (1988)Google Scholar
  22. [Iw]
    Iwaniec, H.: On the order of vanishing of modularL-functions at the critical point, Séminaire de Théorie des Nombres, Bordeaux2, 365–376 (1990)Google Scholar
  23. [Ja 1]
    Jannsen, U.: Continuous Étale Cohomology, Math. Ann.280, 207–245 (1988)Google Scholar
  24. [Ja 2]
    Jannsen, U.: Mixed Motives and AlgebraicK-Theory, Lect. Notes in Math.1400, Springer, Berlin, Heidelberg, New York, 1990Google Scholar
  25. [Kak-Me]
    Kato, K., Messing, W.: syntomic cohomology andp-adic étale cohomology, Tôhoku Math. J.44, 1–9 (1992)Google Scholar
  26. [Ka-Ma]
    Katz, N., Mazur, B.: Arithmetic moduli of elliptic curves, Ann. of Math. Studies108, Princeton Univ. Press, Princeton, 1985Google Scholar
  27. [KaN-Me]
    Katz, N., Messing, W.: Some consequences of the Riemann hypothesis for varieties over finite fields, Invent. Math.,23, 73–77 (1974)Google Scholar
  28. [Ko]
    Kolyvagin, V.A.: Euler systems, in: The Grothendieck Festschrift II, Progress in Mathematics87, Birkhäuser, Boston, Basel, Berlin, 1990, pp. 435–483Google Scholar
  29. [Li]
    Lingen, J. van der: Intersection of Heegner divisors onX 0(N), Minor Thesis, Amsterdam UniversityGoogle Scholar
  30. [M-T-T]
    Mazur, B., Tate, J., Teitelbaum, J.: Onp-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math.84, 1–48 (1986)Google Scholar
  31. [Mu-Mu]
    Murty, V.K., Murty, M.R.: Mean values of derivatives of modularL-series, Ann. of Math.133, 447–475 (1991)Google Scholar
  32. [Ne 1]
    Nekovář, J.: Kolyvagin's method for Chow groups of Kuga-Sato varieties, Invent. Math.107, 99–125 (1992)Google Scholar
  33. [Ne 2]
    Nekovář, J.: Onp-adic height pairings, in: Séminaire de théorie des nombres de Paris 1990/91, Progress in Math.108, (David, S., ed.), Birkhäuser, Boston, 1993, pp. 127–202Google Scholar
  34. [Ne 3]
    Nekovář, J.: Syntomic cohomology andp-adic regulators, in preparationGoogle Scholar
  35. [PR 1]
    Perrin-Riou, B.: FonctionsL p-adiques associées à une forme modulaire et à un corps quadratique imaginaire, J. London Math. Soc.38, 1–32 (1988)Google Scholar
  36. [PR 2]
    Perrin-Riou, B.: Points de Heegner et dérivées de fonctionsL p-adiques, Invent. Math.89, 455–510 (1987)Google Scholar
  37. [PR 3]
    Perrin-Riou, B: Théorie d'Iwasawa et hauteursp-adiques, Invent. Math.109 (1992), 137–185Google Scholar
  38. [ScA 1]
    Scholl, A.J.: Motives for modular forms, Invent. Math.100, 419–430 (1990)Google Scholar
  39. [ScA 2]
    Scholl, A.J.: Height pairings and values ofL-functions, in: Motives, Proceedings of AMS Summer Research Conference held in July 1991, Seattle, Proceedings of Symposia in Pure Mathematics55/I, American Mathematical Society, Providence, Rhode Island, 1994, pp. 571–598Google Scholar
  40. [ScC]
    Schoen, C.: Complex multiplication cycles and a conjecture of Beilinson and Bloch, Trans. A.M.S.339 (1993), 87–115Google Scholar
  41. [ScP 1]
    Schneider, P.:p-adic height pairings I, Invent. Math.69, 401–409 (1982)Google Scholar
  42. [ScP 2]
    Schneider, P.:p-adic height pairings II, Invent. Math.79, 329–374 (1985)Google Scholar
  43. [Se]
    Serre, J.-P.: Cohomologie Galoisienne, Lect. Notes in Math.5, Springer, Berlin, Göttingen, Heidelberg, New York, 1964Google Scholar
  44. [Se-Ta]
    Serre, J.-P., Tate, J.: Good reduction of abelian varieties, Ann. of Math.88, 492–517 (1968)Google Scholar
  45. [Sh]
    Shimura, G.: The Special Values of the Zeta Functions Associated with Cusp Forms, Comm. Pure Appl. Math.39, 783–804 (1976)Google Scholar
  46. [Si]
    Siegel, C.L.: Advanced Analytic Number Theory, Tata Institute for Fundamental Research, Bombay, 1980Google Scholar
  47. [Sk-Za]
    Skoruppa, N.-P., Zagier, D.B.: Jacobi forms and a certain space of modular forms, Invent. Math.94, 113–146 (1988)Google Scholar
  48. [St]
    Sturm, J.: Projections ofC automorphic forms, Bull. AMS2, 435–439 (1980)Google Scholar
  49. [Ta]
    Tate, J.: Relations betweenK 2 and Galois cohomology, Invent. Math.36, 257–274 (1976)Google Scholar
  50. [Wa]
    Waldspurger, J.-L.: Correspondences de Shimura, in: Proc. ICM 1983 Warszawa, pp. 525–531Google Scholar
  51. [Wi]
    Wiles, A.: On ordinary λ-adic representations associated to modular forms, Invent. Math.94, 529–573 (1988)Google Scholar
  52. [SGA 41/2]
    Cohomologie Étale, Lect. Notes in Math.569, Springer, Berlin, Heidelberg, New York, 1977Google Scholar

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© Springer-Verlag 1995

Authors and Affiliations

  • Jan Nekovář
    • 1
  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

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